


Here we generalize our techniques from 2x2 systems to 3x3 systems.












Here we use a 2x2 linear system to show how matrices can be used to streamline the elimination technique.


Here we talk about two operations: union and intersection. These are ways of combining sets to make new sets.


Here we discuss universal sets, or universes, and explain what it means to take a complement of a set with respect to a given universe.


Here we discuss what it means for a set to be empty. We give several examples of empty sets, and make an argument for why we should think of them all as THE Empty Set.


Here we present the idea of subsets. Several examples are given.


Here we give the definition of a set, and give some examples.


Here we finish the warehouse example, by investigating the values of the objective function.


Here we continue the example from the previous video.


Here we introduce the idea of Linear Programming, and begin an example.


Here we work through a word problem about buying tables for a cafeteria. This problem is similar to [4.4, Example 4, pages 244245] in your textbook, so please take a look and compare. Here is the…


Here we continue the example from pt1. This time we use the addition method to verify the coordinates of the last point of the triangle.


Here we graph a system of three inequalities. We also do some algebra to verify the coordinates of a certain point.


Here we introduce the idea of graphing systems of inequalities. A short example is given.


Here we discuss how to graph inequalities in two variables.


Here we introduce interval notation, and give several examples. We also discuss what happens when we take the intersection or the union of two intervals.


Here we simplify and graph a compound inequality.


Here we go through a short example of graphing an inequality on a number line.


Here we introduce inequalities, and discuss an example where dividing by a negative forces us to flip the sign.
